Browsing General by Author "Cohen Graeme"

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Browsing General by Author "Cohen Graeme"

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  • Dartboard Arrangements 
    Cohen Graeme; Tonkes Elliot (International Press, 2001)
    This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and ...
  • Derived sequences 
    Cohen Graeme; Iannucci Douglas (University of Waterloo, Ontario, Canada, 2003)
    We define a multiplicative arithmetic function D by assigning D(pa) = apa-1, when p is a prime and a is a positive integer, and, for n ¸ 1, we set D0(n) = n and Dk(n) = D(Dk-1(n)) when k ¸ 1. We term {Dk(n)}k =0 the ...
  • On perfect totient numbers 
    Iannucci Douglas; Moujie Deng; Cohen Graeme (University of Waterloo, Ontario, Canada, 2003)
  • Superharmonic Numbers 
    Cohen Graeme (Amer Mathematical Soc, 2008)
    Let tau(n) denote the number of positive divisors of a natural number n > 1 and let sigma( n) denote their sum. Then n is superharmonic if sigma(n) vertical bar n(k)tau(n) for some positive integer k. We deduce numerous ...